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It is shown that for the generalized rigid body certain Cartan subalgebras (called of coordinate type) of so(n) are equilibrium points for the rigid body dynamics. In the case of so(4) there are three coordinate type Cartan subalgebras which on a regular adjoint orbit give three Weyl group orbits of equilibria. These coordinate type Cartan subalgebras are… (More)

- Petre Birtea, Ioan Casu
- Appl. Math. Lett.
- 2013

- Petre Birtea, Ioan Casu
- I. J. Bifurcation and Chaos
- 2013

We prove that the study of stability using energy methods strongly depends on the conservation laws considered. We exemplify this by studying stability using Arnold’s method in the case of so(4) free rigid body. Using the classical Mishchenko’s constants of motion we do not obtain satisfactory stability results. We find new constants of motion generated by… (More)

- Petre Birtea, Ioan Casu, Tudor S. Ratiu, Murat Turhan
- J. Nonlinear Science
- 2012

- Árpád Bényi, IOAN CAŞU
- 2009

A quick proof, by construction, of the first part of this result goes as follows: consider a rotation of π/3 radians about the point C that maps point A to point B, and M to M . Clearly, △MCM ′ is equilateral and MM ′ = MC. Since MA = M B, we conclude that △MBM ′ has sides equal to MA,MB, and MC (see Figure 1; all marked angles are equal to π/3 radians).… (More)

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